Overview
This lecture covers the physics of free fall and motion on an inclined plane, focusing on constant acceleration and how to apply kinematic equations to various scenarios.
Free Fall and Constant Acceleration
- Free fall is defined as motion under the influence of gravity alone.
- All objects in free fall, regardless of mass, accelerate downward at a constant rate.
- The acceleration due to gravity is denoted as ( g ) and equals ( 9.80, \text{m/s}^2 ) (to be used in calculations/assignments).
- The direction of gravitational acceleration is always vertically downward.
- ( g ) is positive by definition as a magnitude, but acceleration can be negative depending on coordinate choice.
- Do not call ( g ) "gravity"—it is the acceleration due to gravity, not the gravitational force.
- The value of ( g ) varies on other planets or moons.
Example: Solving a Free Fall Problem
- Example: Dropping a marker from 2 meters above the ground, starting from rest.
- Set origin (y=0) at the ground and time origin at ( t=0 ).
- The kinematic equation used: ( y_1 = y_0 + v_0(t_1 - t_0) + \frac{1}{2}a(t_1 - t_0)^2 ).
- For this case: ( y_1 = 0 ), ( y_0 = 2,m ), ( v_0 = 0 ), ( a = -g ), ( t_0 = 0 ).
- Rearranged equation: ( t_1 = \sqrt{\frac{2 y_0}{g}} ).
- Calculated drop time: ( t_1 = 0.61, \text{seconds} ).
Motion on an Inclined Plane (Inclined Motion)
- Inclined motion refers to objects moving along a ramp with angle ( \theta ).
- Assume a frictionless ramp (motion only under gravity).
- Acceleration along the ramp is ( a = g \sin\theta ).
- The direction of acceleration depends on the orientation of the incline and chosen coordinate system.
- Use standard kinematic equations, substituting ( a ) with ( g \sin\theta ).
Key Terms & Definitions
- Free Fall — Motion under the influence of gravity only.
- Acceleration due to Gravity (( g )) — The constant acceleration of free-falling objects on Earth (( 9.80, \text{m/s}^2 )).
- Kinematic Equation (Constant Acceleration) — ( y_1 = y_0 + v_0(t_1 - t_0) + \frac{1}{2}a(t_1 - t_0)^2 ).
- Inclined Plane — A flat surface tilted at an angle, causing objects to accelerate at ( g \sin\theta ) when frictionless.
Action Items / Next Steps
- Use ( g = 9.80, \text{m/s}^2 ) for all assignments and tests.
- Watch the recommended video linked by the instructor for the feather and bowling ball demo.
- Practice solving free fall and inclined plane problems using kinematic equations.